Electroweak vacuum (in)stability in an inflationary universe

Abstract

Recent analysis shows that if the 125-126 GeV LHC resonance turns out to be the Standard Model Higgs boson, the electroweak vacuum would be a metastable state at 98% C.L. In this paper we argue that, during inflation, the electroweak vacuum can actually be very short-lived, contrary to the conclusion that follows from the flat spacetime analysis. Namely, in the case of a pure Higgs potential the electroweak vacuum decays via the Hawking-Moss transition, which has no flat spacetime analogue. As a result, the Higgs vacuum is unstable, unless the rate of inflation is low enough: H inf 10 9 −10 12 GeV. Models of inflation with such a low rate typically predict negligible tensor perturbations in the cosmic microwave background radiation (CMBR). This is also true for models in which the perturbations are produced by a curvaton field. We also find that if the effective curvature of the Higgs potential at a local maximum (which may be induced by inflaton-Higgs interactions) is large enough, then the decay of the electroweak vacuum is dominated by the Coleman-de Luccia transition. The electroweak vacuum is also short-lived in this case, due to a negative effective self-interaction coupling. Based on our analysis of Higgs vacuum stability during inflation, we conclude that the observation of tensor perturbations by the Planck satellite would provide strong indirect evidence for new physics beyond the Standard Model responsible for stabilisation of the electroweak vacuum.

(Higgs) vacuum decay during inflation

“…The sign of ∆ is fixed by the potential, so that Coleman bounces exist for H < H cr when ∆ < 0, and for H > H cr otherwise. 8 Our potential has V (4) > 0 and thereby ∆ < 0, so that Coleman bounces exist only for H < H cr .…”

“…The Hawking-Moss bounce exists whenever the potential has a barrier, and its action can be easily computed exactly. When the Hubble constant is much smaller than the 8 The expansion of the potential fails for different potentials that involve vastly different mass scales (in particular the ones with a very flat barrier), which need a more careful analysis of higher order terms in eq. (3.2).…”

“…The Higgs field can fluctuate towards values a few orders of magnitude below the Planck scale, for which its potential can be deeper than for the electroweak vacuum [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. If vacuum decay happens during inflation, the regions of true vacuum expand and engulf the whole space [2,18,24].…”

Indirect determinations of the top quark mass

“…The measured SM parameters lie so close to the critical condition for the formation of the large-field minimum that the instability scale can fluctuate from 10 10 GeV to the Planck scale with a variation of M t of merely 2 GeV [1][2][3][4]. Any such small change in M t can have a substantial effect in the evolution of the universe at the inflationary epoch [5][6][7][8][9][10][11][12] and determine the viability of scenarios of Higgs inflation [13]. A more precise determination of M t will add important information to our knowledge of particle physics and cosmology.…”

“…By power counting we estimate the coefficient of the dimension-5 operator to be of order |V td | 2 y 3 t /(16π 2 M t ), which corresponds again to a quadratic sensitivity on M t . Explicit calculation of the diagram in figure 1 gives a correction to the 6) where in the SM at tree level…”